Problem: Factor the following expression: $27x^2 - 3$
We can start by factoring a ${3}$ out of each term: $ {3}({9x^2} - {1})$ The second term is of the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as ${3}({a} + {b}) ({a} - {b})$ What are the values of $a$ and $b$ $ a = \sqrt{9x^2} = 3x$ $ b = \sqrt{1} = 1$ Use the values we found for $a$ and $b$ to complete the factored expression, ${3}({a} + {b}) ({a} - {b})$ So we can factor the expression as: ${3}({3x} + {1}) ({3x} - {1})$